Signal detection problems

Abstract

In this dissertation two distinct approaches are considered in order to obtain signal detection schemes when the signal-to-noise ratio approaches zero. The first part of this dissertation is devoted to the investigation of the performance analysis of the locally optimum detector for composite signals in purely-additive noise. To obtain the performance characteristics of the locally optimum detector for composite signals, we consider two calssical methods, the asymptotic performance and finite sample-size performance characteristics. Performance characteristics of the linear correlator detector, the sign correlator detector, the locally optimum stochastic-signaldetector, and the square-law detector for composite signals are also obtained, and then compared to those of the locally optimum detector. As a new approach to signal detection, we obtain detection schemes based on fuzzy testing of statistical hypothesis assuming that fuzziness is involved in the observations. We first obtain the fuzzy set theoretic extension of the generalized Neyman-Pearson lemma and define the locally optimum fuzzy test. Based on the results we then consider applications of fuzzy testing of statistical hypothesis to weak known and stochastic signal detection problems. Specifically, locally optimum fuzzy detector test statistics and some properties on the locally optimum fuzzy nonlinearities are obtained. Performance characteristics of the locally optimum fuzzy detector are also examined and some discussions are made.